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Volumn 24, Issue 1, 1996, Pages 255-286

Reml estimation: Asymptotic behavior and related topics

Author keywords

ANOVA; Asymptotic normality; Consistency; Mixed models; MLE; Restricted maximum likelihood

Indexed keywords


EID: 0030559451     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1033066209     Document Type: Article
Times cited : (148)

References (44)
  • 1
    • 0000531364 scopus 로고
    • Asymptotically efficient estimation of covariance matrices with linear structure
    • ANDERSON, T. W. (1973). Asymptotically efficient estimation of covariance matrices with linear structure. Ann. Statist. 1 135-141.
    • (1973) Ann. Statist. , vol.1 , pp. 135-141
    • Anderson, T.W.1
  • 2
    • 0010940842 scopus 로고
    • Estimation and hypothesis testing for collection of autoregressive time series
    • AZZALINI, A. (1984). Estimation and hypothesis testing for collection of autoregressive time series. Biometrika 71 85-90.
    • (1984) Biometrika , vol.71 , pp. 85-90
    • Azzalini, A.1
  • 3
    • 0000072546 scopus 로고
    • On a formula for the distribution of the maximum likelihood estimator
    • BARNDORFF-NIELSEN, O. (1983). On a formula for the distribution of the maximum likelihood estimator. Biometrika 70 343-365.
    • (1983) Biometrika , vol.70 , pp. 343-365
    • Barndorff-Nielsen, O.1
  • 4
    • 0010876221 scopus 로고
    • Estimation in semiparametric model
    • C. R. Rao, ed. North-Holland, Amsterdam
    • BICKEL, P. J. (1993). Estimation in semiparametric model. In Multivariate analysis: Future direction (C. R. Rao, ed.) 55-73. North-Holland, Amsterdam.
    • (1993) Multivariate Analysis: Future Direction , pp. 55-73
    • Bickel, P.J.1
  • 5
    • 0001575010 scopus 로고
    • Asymptotic behavior of MINQUE-type estimators of variance components
    • BROWN, K. G. (1976). Asymptotic behavior of MINQUE-type estimators of variance components. Ann. Statist. 4 746-754.
    • (1976) Ann. Statist. , vol.4 , pp. 746-754
    • Brown, K.G.1
  • 6
    • 0040707600 scopus 로고
    • Hermitian matrix inequalities and a conjecture
    • CHAN, N. N. and KWONG, M. K. (1985). Hermitian matrix inequalities and a conjecture. Amer. Math. Monthly 92 533-541.
    • (1985) Amer. Math. Monthly , vol.92 , pp. 533-541
    • Chan, N.N.1    Kwong, M.K.2
  • 8
    • 0017743528 scopus 로고
    • A note on the estimation of the parameters of autoregressive-moving average process
    • COOPER, D. M. and THOMPSON, R. (1977). A note on the estimation of the parameters of autoregressive-moving average process. Biometrika 64 625-628.
    • (1977) Biometrika , vol.64 , pp. 625-628
    • Cooper, D.M.1    Thompson, R.2
  • 9
    • 0001846042 scopus 로고
    • REML estimation in empirical bayes smoothing of census undercount
    • CRESSIE, N. (1992). REML estimation in empirical Bayes smoothing of census undercount. Survey Methodology 18 75-94.
    • (1992) Survey Methodology , vol.18 , pp. 75-94
    • Cressie, N.1
  • 10
    • 38249002211 scopus 로고
    • The asymptotic distribution of REML estimators
    • CRESSIE, N. and LAHIRI, S. N. (1993). The asymptotic distribution of REML estimators. J. Multivariate Anal. 45 217-233.
    • (1993) J. Multivariate Anal. , vol.45 , pp. 217-233
    • Cressie, N.1    Lahiri, S.N.2
  • 11
    • 0039522274 scopus 로고
    • Asymptotic optimality of restricted maximum likelihood estimates for the mixed model
    • DAS, K. (1979). Asymptotic optimality of restricted maximum likelihood estimates for the mixed model. Calcutta Statist. Assoc. Bull. 28 125-142.
    • (1979) Calcutta Statist. Assoc. Bull. , vol.28 , pp. 125-142
    • Das, K.1
  • 12
    • 34250109475 scopus 로고
    • A central limit theorem for generalized quadratic forms
    • DE JONG, P. (1987). A central limit theorem for generalized quadratic forms. Probab. Theory Related Fields 75 261-277.
    • (1987) Probab. Theory Related Fields , vol.75 , pp. 261-277
    • De Jong, P.1
  • 13
    • 0001263213 scopus 로고
    • Noncentral limit theorems for quadratic forms in random variables having long-range dependence
    • Fox, R. and TAQQU, M. S. (1985). Noncentral limit theorems for quadratic forms in random variables having long-range dependence. Ann. Probab. 13 428-446.
    • (1985) Ann. Probab. , vol.13 , pp. 428-446
    • Fox, R.1    Taqqu, M.S.2
  • 14
    • 0023468531 scopus 로고
    • Residual maximum likelihood (REML) estimation of a neighbour model for field experiments
    • GLEESON, A. C. and CULLIS, B. R. (1987). Residual maximum likelihood (REML) estimation of a neighbour model for field experiments. Biometrics 43 277-287.
    • (1987) Biometrics , vol.43 , pp. 277-287
    • Gleeson, A.C.1    Cullis, B.R.2
  • 15
    • 77956888108 scopus 로고
    • Linear models for field trials, smoothing and cross-validation
    • GREEN, P. J. (1985). Linear models for field trials, smoothing and cross-validation. Biometrika 72 527-537.
    • (1985) Biometrika , vol.72 , pp. 527-537
    • Green, P.J.1
  • 16
    • 0038929636 scopus 로고
    • Or the asymptotic distribution of quadratic forms in uniform order statistics
    • GUTTORP, P. and LOCKHART, R. A. (1988). Or the asymptotic distribution of quadratic forms in uniform order statistics. Ann. Statist. 16 433-449.
    • (1988) Ann. Statist. , vol.16 , pp. 433-449
    • Guttorp, P.1    Lockhart, R.A.2
  • 19
    • 0014099014 scopus 로고
    • Maximum likelihood estimation for the mixed analysis of variance model
    • HARTLEY, H. O. and RAO, J. N. K. (1967). Maximum likelihood estimation for the mixed analysis of variance model. Biometrika 54 93-108.
    • (1967) Biometrika , vol.54 , pp. 93-108
    • Hartley, H.O.1    Rao, J.N.K.2
  • 20
    • 85041975654 scopus 로고
    • Bayesian inference for variance components using only error contrasts
    • HARVILLE, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61 383-385.
    • (1974) Biometrika , vol.61 , pp. 383-385
    • Harville, D.A.1
  • 21
    • 84890913931 scopus 로고
    • Maximum likelihood approaches to variance components estimation and related problems
    • HARVILLE, D. A. (1977). Maximum likelihood approaches to variance components estimation and related problems. J. Amer. Statist. Assoc. 72 320-340.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 320-340
    • Harville, D.A.1
  • 23
    • 0000932881 scopus 로고
    • Variance components analysis: A selective literature survey
    • KHURI, A. I. and SAHAI, H. (1985). Variance components analysis: a selective literature survey. Internat. Statist. Rev. 53 279-300
    • (1985) Internat. Statist. Rev. , vol.53 , pp. 279-300
    • Khuri, A.I.1    Sahai, H.2
  • 24
    • 0020333131 scopus 로고
    • Random effects models for longitudinal data
    • LAIRD, N. M. and WARE, J. M. (1982). Random effects models for longitudinal data. Biometrics 38 963-974.
    • (1982) Biometrics , vol.38 , pp. 963-974
    • Laird, N.M.1    Ware, J.M.2
  • 26
    • 0001143341 scopus 로고
    • On the existence and uniqueness of the maximum likelihood estimates of a vector-valued parameter in fixed-size samples
    • MÄKELÄINEN, T., SCHMIDT, K. and STYAN, G. P. H. (1981). On the existence and uniqueness of the maximum likelihood estimates of a vector-valued parameter in fixed-size samples. Ann. Statist. 9 758-767.
    • (1981) Ann. Statist. , vol.9 , pp. 758-767
    • Mäkeläinen, T.1    Schmidt, K.2    Styan, G.P.H.3
  • 27
    • 0001065876 scopus 로고
    • Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance
    • MILLER, J. J. (1977). Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance. Ann. Statist. 5 746-762.
    • (1977) Ann. Statist. , vol.5 , pp. 746-762
    • Miller, J.J.1
  • 28
    • 0001831031 scopus 로고
    • Consistent estimates based on partially consistent observations
    • NEYMAN, J. and SCOTT, E. (1948). Consistent estimates based on partially consistent observations. Econometrika 16 1-32.
    • (1948) Econometrika , vol.16 , pp. 1-32
    • Neyman, J.1    Scott, E.2
  • 29
    • 77956889208 scopus 로고
    • Recovery of interblock information when block sizes are unequal
    • PATTERSON, H. D. and THOMPSON, R. (1971). Recovery of interblock information when block sizes are unequal. Biometrika 58 545-554.
    • (1971) Biometrika , vol.58 , pp. 545-554
    • Patterson, H.D.1    Thompson, R.2
  • 30
    • 21344480147 scopus 로고
    • Incidental versus random nuisance parameters
    • PFANZAGL, J. (1993). Incidental versus random nuisance parameters. Ann. Statist. 21 1663-1691.
    • (1993) Ann. Statist. , vol.21 , pp. 1663-1691
    • Pfanzagl, J.1
  • 32
    • 84990551091 scopus 로고
    • Asymptotic properties of restricted maximum likelihood (REML) estimates for hierarchical mixed linear models
    • RICHARDSON, A. M. and WELSH, A. H. (1994). Asymptotic properties of restricted maximum likelihood (REML) estimates for hierarchical mixed linear models. Austral. J. Statist. 36 31-43.
    • (1994) Austral. J. Statist. , vol.36 , pp. 31-43
    • Richardson, A.M.1    Welsh, A.H.2
  • 33
    • 0001998938 scopus 로고
    • Estimation and use of variance components
    • ROBINSON, D. L. (1987). Estimation and use of variance components. The Statistician 36 3-14.
    • (1987) The Statistician , vol.36 , pp. 3-14
    • Robinson, D.L.1
  • 34
    • 0012492650 scopus 로고
    • Contributions to asymptotic theory in regression models with linear covariance structure
    • SCHMIDT, W. H. and THRUM, R. (1981). Contributions to asymptotic theory in regression models with linear covariance structure. Math. Operationsforsch. Statist. Ser. Statist. 12 243-269.
    • (1981) Math. Operationsforsch. Statist. Ser. Statist. , vol.12 , pp. 243-269
    • Schmidt, W.H.1    Thrum, R.2
  • 36
    • 0040113899 scopus 로고
    • Cumulants and partition lattices IV: A.s. convergence of generalized k-statistics
    • SPEED, T. P. (1986). Cumulants and partition lattices IV: a.s. convergence of generalized k-statistics. J. Austral. Math. Soc. 41 79-94.
    • (1986) J. Austral. Math. Soc. , vol.41 , pp. 79-94
    • Speed, T.P.1
  • 37
    • 0041512328 scopus 로고
    • Comment on "that BLUP is a good thing - The estimation of random effects" by G. K. Robinson
    • SPEED, T. P. (1991). Comment on "That BLUP is a good thing - The estimation of random effects" by G. K. Robinson. Statist. Sci. 6 42-44.
    • (1991) Statist. Sci. , vol.6 , pp. 42-44
    • Speed, T.P.1
  • 38
    • 0000899174 scopus 로고
    • Explicit maximum likelihood estimates from balanced data in the mixed model of the analysis of variance
    • SZATROWSKI, T. H. and MILLER, J. J. (1980). Explicit maximum likelihood estimates from balanced data in the mixed model of the analysis of variance. Ann. Statist. 8 811-819.
    • (1980) Ann. Statist. , vol.8 , pp. 811-819
    • Szatrowski, T.H.1    Miller, J.J.2
  • 39
    • 0000139505 scopus 로고
    • The problem of negative estimates of variance components
    • THOMPSON, W. A., JR. (1962). The problem of negative estimates of variance components. Ann. Math. Statist. 33 273-289.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 273-289
    • Thompson W.A., Jr.1
  • 40
    • 84985582667 scopus 로고
    • A conditional derivation of residual maximum likelihood
    • VERBYLA, A. P. (1990). A conditional derivation of residual maximum likelihood. Austral. J. Statist. 32 227-230.
    • (1990) Austral. J. Statist. , vol.32 , pp. 227-230
    • Verbyla, A.P.1
  • 42
    • 0001255679 scopus 로고
    • Asymptotic properties of maximum likelihood estimators in some nonstandard cases
    • WEISS, L. (1971). Asymptotic properties of maximum likelihood estimators in some nonstandard cases. J. Amer. Statist. Assoc. 66 345-350.
    • (1971) J. Amer. Statist. Assoc. , vol.66 , pp. 345-350
    • Weiss, L.1
  • 43
    • 0040707543 scopus 로고
    • Asymptotic normality of the ANOVA estimates of components of variance in the nonnormal, unbalanced hierarchal mixed model
    • WESTFALL, P. H. (1986). Asymptotic normality of the ANOVA estimates of components of variance in the nonnormal, unbalanced hierarchal mixed model. Ann. Statist. 14 1572-1582.
    • (1986) Ann. Statist. , vol.14 , pp. 1572-1582
    • Westfall, P.H.1
  • 44
    • 0000723104 scopus 로고
    • Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms
    • ZELLNER, A. (1976). Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms. J. Amer. Statist. Assoc. 71 400-405.
    • (1976) J. Amer. Statist. Assoc. , vol.71 , pp. 400-405
    • Zellner, A.1


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